According to Newton's law of universal gravitation, the magnitude of the gravitational force between two point masses depends on which two factors?

• A. The densities of the objects and their surface areas in contact
• B. The sum of the two masses and the distance between their centers (inverse-first-power dependence)
• C. The product of the two masses and the distance between their centers (inverse-square dependence)
• D. The product of the two masses and the square of the distance between their centers (direct-square dependence)

Answer: (C)

Verified step by step guidance

1. Recall Newton's law of universal gravitation, which states that the gravitational force \(F\) between two point masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
2. Express the law mathematically as: \(F = G \frac{m_1 \times m_2}{r^2}\), where \(m_1\) and \(m_2\) are the masses, \(r\) is the distance between their centers, and \(G\) is the gravitational constant.
3. Understand that the force depends on the product of the two masses, meaning if either mass increases, the force increases proportionally.
4. Recognize the inverse-square dependence on distance, meaning if the distance doubles, the force becomes one-fourth as strong.
5. Note that the densities, surface areas, or sums of masses are not factors in this law; only the product of masses and the square of the distance between centers matter.